eacher Supplemen o Operaion Comics, Issue #5 he purpose of his supplemen is o provide conen suppor for he mahemaics embedded ino he fifh issue of Operaion Comics, and o show how he mahemaics addresses he conen sandards provided by he Naional Council of eachers of Mahemaics (NCM) for grades 3 5 and 6 8. he mahemaics in his issue is a lile ligh in comparison o he oher issues, as he main purpose of he issue is o explain he origin of Wonderguy. owever, in he course of explaining his origins, we are able o involve some science, specifically geneics and Punne squares, and some probabiliy. he mahemaics used in his issue addresses boh he NCM sandard for problem solving and he NCM sandard for reasoning and proof, for boh grade ranges, in addiion o he sandards addressed below. Punne Squares and Probabiliy he explanaion we give for Wonderguy s immense srengh is ha boh of his parens had heir geneics alered slighly o where hey each carried a leas one recessive gene for super-srengh. Claire and Dillon, having jus recenly used Punne squares in heir science class, demonsrae how ha mean ha here was a bes only a 1-in-4 chance (25%) ha his parens had an offspring wih super-srengh, as shown in he figure.
2 We are able o illusrae ha he probabiliy of muliple independen evens is he produc of he individual probabiliies by considering he possibiliy ha having super-srengh relies on having more han one recessive gene in place. he suden workshees will reinforce his idea by having sudens consruc Punne squares for muliple siuaions. Using Punne Squares he firs suden supplemen ha accompanies his issue has he sudens consrucing heir own Punne squares and reading probabiliies from he resuls. Noe ha he resuls only hold if he genes are equally-likely o be passed on o heir offspring. Soluions are given below. 1) he Punne square in his case would look like he following. 1) Suppose one paren is supersrong () and he oher does no carry he recessive gene (). he probabiliy ha heir offspring has super-srengh is 0.
3 2) he Punne square in his case would look like he following. 2) Suppose one paren is supersrong () and he oher does carry he recessive gene (). he probabiliy ha heir offspring has super-srengh is 1 2. 3) he Punne square in his case would look like he following. 3) Suppose one paren carries he recessive gene () and he oher does no (). he probabiliy ha heir offspring has super-srengh is 0. Super-ricky! he probabiliies ha he offspring does no have super-srengh in each of he 1 problems is 1) 1, 2), and 3) 1. In each case, he probabiliies ha he offspring does have 2 super-srengh and does no sum o 1. wo Independen Genes for Super-Srengh #1 he second suden supplemen ha accompanies his issue has he sudens consrucing heir own Punne squares where more han one genoype is involved, and reading probabiliies from he resuls. Noe ha he resuls only hold if he genes are equally-likely o be passed on o heir offspring. Soluions are given below.
4 Sep 1: he ree diagram showing he possible gene combinaions sen o an offspring from one paren is shown below. Firs Gene Second Gene Possibiliies h h h Sep 2: he Punne square in his case would look like he following. h h h h h h h h h hh hh h h h hh hh Only he hh genoype would have super-srengh, so he probabiliy is 1. Noice ha his is 16 he produc of he probabiliies for each genoype, 1 4 1 4 = 1 16. Super-ricky! he probabiliy ha heir offspring will carry a leas one recessive gene, bu no have super-srengh, is 14 16 = 7. he probabiliy ha heir offspring will no have a recessive 8 gene is 1. he sum of he probabiliies is 1. 16 wo Independen Genes for Super-Srengh #2 he hird suden supplemen ha accompanies his issue has he sudens consrucing heir own Punne squares where more han one genoype is involved, and reading probabiliies from he resuls. Noe ha he resuls only hold if he genes are equally-likely o be passed on o heir offspring. Soluions are given below.
5 Sep 1: he ree diagram showing he possible gene combinaions sen o an offspring from he faher is shown below. Firs Gene Second Gene Possibiliies h h h he ree diagram showing he possible gene combinaions sen o an offspring from he moher is shown below. Firs Gene Second Gene Possibiliies Sep 2: he Punne square in his case would look like he following. h h h h h h h h h h Only he hh genoype would have super-srengh, so he probabiliy is 0. Super-ricky! If hree doubly-recessive gene pairs were needed o produce an offspring wih super-srengh, and each paren had he genoype hrr, hen each paren could poenially send heir offspring he gene combinaions R, R, r, r, hr, hr, hr, and hr. hus, he Punne square for his scenario would be as follows.
6 R R r r hr hr hr hr R RR RR Rr Rr hrr hrr hrr hrr R RR RR Rr Rr hrr hrr hrr hrr r Rr Rr rr rr hrr hrr hrr hrr r Rr Rr rr rr hrr hrr hrr hrr hr hrr hrr hrr hrr hhrr hhrr hhrr hhrr hr hrr hrr hrr hrr hhrr hhrr hhrr hhrr hr hrr hrr hrr hrr hhrr hhrr hhrr hhrr hr hrr hrr hrr hrr hhrr hhrr hhrr hhrr 1 Only he hhrr genoype would have super-srengh, so he probabiliy is. Noice ha his 64 is he produc of he probabiliies for hree separae genoypes, 1 4 1 4 1 4 = 1 64. NCM Sandards he couning of oucomes o find probabiliies addresses he NCM sandard for daa analysis and probabiliy for grades 3 5, which says ha in grades 3 5, all sudens should propose and jusify conclusions and predicions ha are based on daa and design sudies o furher invesigae he conclusions or predicions, describe evens as likely or unlikely and discuss he degree of likelihood using such erms as cerain, equally likely, and impossible, predic he probabiliy of oucomes of simple experimens and es he predicions, and undersand ha he measure of he likelihood of an even can be represened by a number from 0 o 1. I also addresses he NCM sandard for daa analysis and probabiliy for grades 6 8, which says ha in grades 6 8, all sudens should compue probabiliies for simple compound evens, using such mehods as organized liss, ree diagrams, and area models. In addiion o he NCM sandards, he consrucion of Punne squares helps mee core sandards in he science curriculum, bu we will resric our commens o jus he mah sandards. One las noe... While my purpose here is o produce a comic book wih embedded mahemaical conen, and mahemaics is my background, I did endeavor o wrie a good sory, and hopefully, he comics can be used for heir lierary elemens as well. he following are a few examples of suble hings a work in he sory. he sory references a super-soldier program, which was previously referenced in anoher issue, Operaion Comics #3: No Your Average Ca, wih he villain he Cheeah, who was also a scienis waning o improve upon sandard human abiliies. he noion of having such a program could lead o a philosophical discussion regarding he ehics of having such a program.
We ge o see Wonderguy as a child in his issue, and learn ha he was born wih his grea srengh. his could lead o a discussion of wheher always being exra srong had any affec on how hard he younger Wonderguy acually pursued academics while he was in school. Wha would have been he ramificaions if Wonderguy s parens had no hidden he fac ha he was super-srong as a child? his documen, as wih he suden supplemens, is a work in progress. Please conac me wih correcions or suggesions, and I will make he needed changes. hanks for inviing Wonderguy ino your classrooms, and please encourage your sudens o conac me wih heir commens and suggesions for fuure episodes. 7